Related papers: CRT and Fixed Patterns in Combinatorial Sequences

Transformer has become ubiquitous in the deep learning field. One of the key ingredients that destined its success is the self-attention mechanism, which allows fully-connected contextual encoding over input tokens. However, despite its…

The identification of continuous-time (CT) systems from discrete-time (DT) input and output signals, i.e., the sampled data, has received considerable attention for half a century. The state-of-the-art methods are parametric methods and…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

Modern sentence encoders are used to generate dense vector representations that capture the underlying linguistic characteristics for a sequence of words, including phrases, sentences, or paragraphs. These kinds of representations are ideal…

We consider a strictly stationary and ergodic sequence of random elements taking values in some Hilbert space. Our target is to study the weak convergence of the discrete Fourier transforms under sharp conditions. As a side-result we obtain…

Recently, discriminatively learned correlation filters (DCF) has drawn much attention in visual object tracking community. The success of DCF is potentially attributed to the fact that a large amount of samples are utilized to train the…

Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…

Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity,…

Learning to control the structure of sentences is a challenging problem in text generation. Existing work either relies on simple deterministic approaches or RL-based hard structures. We explore the use of structured variational…

The theorems of density functional theory (DFT) and reduced density matrix functional theory (RDMFT) establish a bijective map between the external potential of a many-body system and its electron density or one-particle reduced density…

Groundstates of 1+1d conformal field theories (CFTs) satisfy a local entropic condition called the vector fixed point equation. This condition is surprisingly well satisfied by groundstates of quantum critical lattice models even at small…

This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by…

We introduce mixed model trace regression (MMTR), a mixed model linear regression extension for scalar responses and high-dimensional matrix-valued covariates. MMTR's fixed effects component is equivalent to trace regression, with an…

In pulsed Doppler radars, the classic Chinese remainder theorem (CCRT) is a common method to resolve Doppler ambiguities caused by fast-moving targets. Another issue concerning high-velocity targets is related to the loss in the…

Density functional theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically…

We discuss several applications of the recently proposed combined nonlinear-condensation transformation (CNCT) for the evaluation of slowly convergent, nonalternating series. These include certain statistical distributions which are of…

Structural Causal Models (SCMs) offer a principled framework to reason about interventions and support out-of-distribution generalization, which are key goals in scientific discovery. However, the task of learning SCMs from observed data…

This work explores the scope of Frequent Sequence Mining in the domain of Lossy Image Compression. The proposed work is based on the idea of clustering pixels and using the cluster identifiers in the compression. The DCT phase in JPEG is…

Generating visual layouts is an essential ingredient of graphic design. The ability to condition layout generation on a partial subset of component attributes is critical to real-world applications that involve user interaction. Recently,…

CRDTs are distributed data types that make eventual consistency of a distributed object possible and non ad-hoc. Specifically, state-based CRDTs ensure convergence through disseminating the entire state, that may be large, and merging it to…